The Nineteenth Byte

Let's say you have six possible values for a column {1,2,3,4,5,6}, and you know that 90% of the values are 1.
Original condition: A<>1 AND A<>2 AND A<>3
Modified condition: A=4 OR A=5 OR A=6 -- or A IN (4,5,6)
The original condition should short circuit on the first condition 90% of the time. The second condition will have to check all three conditions 90% of the time. To a programmer with no real training in SQL performance tuning, the first should be faster.

Nathan Merrill

the second is writing a program that tiles for you

which I'm about to post about

TimmyD

Also, another variation on @MartinBüttner's 5/8 tiling:

1110
1101
1110
0010

Zgarb

Okay, cool. I know people who are working on this type of stuff.

Rainbolt

@ChrisJester-Young It's probably not surprising to a SQL veteran who knows the difference between seeks and scans and how indexes can impact performance. I'm still learning.

Martin Büttner

@NathanMerrill I don't quite understand what your input is now

Nathan Merrill

3:54 PM

@MartinBüttner I'm going to use this ok?

Martin Büttner

sure?

Nathan Merrill

its a good example of tiling that isn't grid based

orthogonal based?

not sure how to term that

my input is a string

Martin Büttner

"non-rectangular prototile"?

Nathan Merrill

lol

that and the fact that the tiling isn't (0,y), (x,0)

bah, mis-enters

Martin Büttner

oh right

@NathanMerrill what does that string represent though

Nathan Merrill

3:57 PM

I'll sandbox it

Martin Büttner

very good idea ;)

Stefnotch

I am working on a JS interpreter for a language (Labyrinth)...
What should I use to do each step?
a) a while loop
b) a for loop
c) setInterval (Using that one right now)
d) requestAnimationFrame (I doubt I could use that)
e) a web worker
f) something else?

Martin Büttner

unless you're going to animate the execution, use a while loop

Stefnotch

Ok! :D

(But a for loop is shorter, goto is cooler...and web workers sound fancy... :P )

Martin Büttner

> goto is cooler

wat

> for loop is shorter

wat

web workers do sound fancy, I'll give you that

Nathan Merrill

4:03 PM

0

A: Sandbox for Proposed Challenges

Tiler In this challenge, you need to take a string and tile it. For example: abc abcdefabcdef def -> cdefabcdefab efabcdefabcd You will be given 2 inputs (either via function parameter or STDIN): a list of offsets, and a string to tile. The offsets will be in (x,y) for...

Stefnotch

for(;;)
while(!0)

So, for loops are way shorter!

(And I like dinosaurs..)

TimmyD

while(1) doesn't work?

not that it's shorter than for(;;), but still

Stefnotch

Oh, that does work... :D

Martin Büttner

@Stefnotch outside of golfing for(;;) is only cool in C/C++, provided you add a macro #define ever ;;

Nathan Merrill

I'd rather #define ever (;;)

Martin Büttner

4:07 PM

does that work? I thought the preprocessor only touches separate tokens

but maybe it's even dumber than that

Nathan Merrill

no idea

Stefnotch

XD

TimmyD

I keep running into variations on the 5/8 tilings ...

Stefnotch

Can you "override" goto with #define?

Martin Büttner

@NathanMerrill I'm pretty sure it doesn't break up tokens... that would wreak all sorts of havoc...

@Stefnotch you can do worse things: stackoverflow.com/a/771974/1633117

Nathan Merrill

4:09 PM

ok. I thought the preprocessor was before tokenization

Stefnotch

#define a bb
#define b aa
Is that even worse?

Martin Büttner

@NathanMerrill I think it does its own tokenisation, which is a bit different: gcc.gnu.org/onlinedocs/cpp/Tokenization.html#Tokenization

@Stefnotch not really.

New Sandboxed Posts

0

A: Sandbox for Proposed Challenges

Tiler In this challenge, you need to take a string and tile it. For example: abc abcdefabcdef def -> cdefabcdefab efabcdefabcd You will be given 2 inputs (either via function parameter or STDIN): a list of offsets, and a string to tile. The offsets will be in (x,y) for...

Martin Büttner

@NathanMerrill you'll need to come up with 10 more characters for the title ;)

oh now I see what you mean

wouldn't it be more interesting to provide only the prototile and ask for a tiling if possible?

i.e. make the answers figure out a valid offset

New Main Posts

0

Q: An alphabet position quickie to motivate us all

It has been said, or copied from http://ifunny.co/fun/SiQ7PlRR3 rather, that if... A B C D E F G H I J K L M N O P Q R S T U V W X Y Z equals... 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 then... K + N + O + W + L + E + D + G + E 11 + 14 + 15 + 23 + 12 + 5 +...

Martin Büttner

4:14 PM

(and require a that the tiling is gap free, or it should indicate if no gap-free tiling is possible)

Sherlock9

I have an idea: You all remember the question: count the number of sums of squares, right?

Two input numbers, n and p, where the question is to check what is the minimum number of p-th powers that are needed to sum to n

Like 7 needs 4 squares, n=7 p=2

I'll need to come up with some large test cases for things like cubes, 4th powers and 5th powers, but for now, what do you all think?

Martin Büttner

sure why not?

Sherlock9

Excellent. I'll go round up some test cases

Nathan Merrill

@MartinBüttner How would it deal with this:

abc
 def

there are two totally valid tilings

actually, more than that

Calvin's Hobbies

Even color codes work :D (PPCG Playground)

Zgarb

4:26 PM

@Sherlock9 related

(in Wikipedia, not PPCG)

Sherlock9

@Zgarb Yep. It's where I got the idea

@Zgarb I'm thinking of allowing negative cubes in there, though

Nathan Merrill

so many people are upvoting my Weakest link challenge, but I've only received 2 answers :(

Optimizer

maybe you are the weakest link?

Martin Büttner

@NathanMerrill I'd accept any tiling that only involves translation

@Zgarb Do you happen to know if there are some simple conditions a polyomino has to fulfil to be able to tile the plane without gaps (and without rotating or reflecting it).

Zgarb

4:45 PM

@MartinBüttner Hmm, nothing comes to mind right now.

This gives a sufficient condition.

Martin Büttner

interesting. that one seems to allow rotations though.

(so for it to be sufficient, it might actually require rotations)

Zgarb

Okay, here's a characterization and n^2 algorithm: lama.univ-savoie.fr/~vuillon/IanRAIRO.pdf

New Main Posts

0

Q: Hexagonal maze time!

Time for another maze challenge, but not as you know it. The rules for this challenge are a little different than most of this kind. The tile types are defined as follows: S: The location on the maze you start at E: The location you are trying to get to 0: Wall that you can't cross +: Floor th...

code-golf maze

Optimizer

@Zgarb llama*

4

Zgarb

"A polyomino P tiles the plane by translations if and only if the boundary word b(P) is equal up to a cyclic permutation of the symbols to X Y Z X' Y' Z' where one of the variables in the factorization may be empty."

@Optimizer Their logo is a llama: lama.univ-savoie.fr/index.php

Nathan Merrill

4:54 PM

@MartinBüttner does it make more sense to have them output the 20x20 square, or a list of offsets?

Martin Büttner

I liked the idea of outputting the tiling, if possible.

Nathan Merrill

I like the 20x20 because it is more human-readable

but the offsets is easily extendable

Martin Büttner

make it 30x30 and it should be big enough to cover any test cases a solution will be able to handle in a reasonable amount of time :P

@Zgarb Thanks for digging that up. Any luck for non-contiguous polyominoes? (Or whatever you'd call them in that case.)

Calvin's Hobbies

Someone else code something... coderpad.io/GMD6794F

Optimizer

]y?

Zgarb

5:00 PM

@MartinBüttner There's probably an algebraic characterization, but I can't recall one right now.

TimmyD

@Calvin'sHobbies print("something")

Optimizer

code("something")

TimmyD

Traceback (most recent call last):
File "prog.py", line 1, in <module>
NameError: name 'code' is not defined

Stefnotch

What is the best way to have a billion images in a billion places in Javascript?

TimmyD

@Stefnotch jQuery

5

Stefnotch

5:07 PM

(I don't like JQuery...)

Optimizer

prototype.js

Stefnotch

1 million libraries later

CSᵠ

@Stefnotch Error parsing question.

Stefnotch

Ok, let me rephrase that:
What is the WORST way to have a billion images in a billion places in Javascript?

TimmyD

I'm also pretty sure you'd hit a browser out-of-memory error well before you hit 1 billion images loaded, regardless of what JavaScript code you were using ...

Stefnotch

5:12 PM

(I tend to exaggerate...)

Zgarb

@MartinBüttner citeseerx.ist.psu.edu/viewdoc/…

bkul

Arcyou needs better string handling...

Zgarb

Algorithms for when the size of the tile is a prime number or 4

CSᵠ

@Stefnotch array filled with a billion image URI's (pick only short links), then ajax load in a loop each one replacing the previous, few seconds timer, or smth. would requite ~20GB ram give or take another 20

TimmyD

@Stefnotch And I tend to read things literally when it allows me to be a sarcastic wise-ass while doing so. :D

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:18 PM

Hey guys I'm trying to do operator overloading. What should "a string, squared" be?

(And the square roots of lists and strings :P)

Stefnotch

Maybe some magic string compression algorithm that doesn't get described in the specs?

TimmyD

Square of a string? Maybe the string concatenated (string.length) number of times?

Cᴏɴᴏʀ O'Bʀɪᴇɴ

That makes sense. Thanks ^

@Stefnotch Haha, nice

Martin Büttner

@Zgarb wow, thank you

anOKsquirrel

needs more llama

Stefnotch

5:23 PM

Ok, fixed!

Zgarb

@MartinBüttner It seems that the general case is still an open problem.

CSᵠ

not enough jQuery!

anOKsquirrel

llama*

quintopia

@NathanMerrill I asked your tiling question on quora too, just to see if any over there is smrt.

Nathan Merrill

people still use quora?

TimmyD

5:24 PM

^

^

^

guys.

that was exactly what i said to myself about SE before i showed up here

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@CSᵠ ಠ_ಠ

@MartinBüttner Mine was a legit caret

anOKsquirrel

5:25 PM

mine too

Cᴏɴᴏʀ O'Bʀɪᴇɴ

array / (anything) = ?

TimmyD

Really tempted to ^ the "mine too" ...

CSᵠ

@output?

quintopia

@CᴏɴᴏʀO'Bʀɪᴇɴ slice

or chop

Nathan Merrill

@MartinBüttner looks good?

0

A: Sandbox for Proposed Challenges

Tiler In this challenge, you need to take a string and tile it. For example: abc abcdefabcdef def -> cdefabcdefab efabcdefabcd You will be given a string to tile either via function parameter or STDIN. Spaces in the tile are considered "blank" and can be overwritten by...

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:26 PM

@quintopia "chop"?

Nathan Merrill

any other interesting tilings you can think of?

Cᴏɴᴏʀ O'Bʀɪᴇɴ

As in, at every nth index?

Martin Büttner

@NathanMerrill one second

quintopia

@CᴏɴᴏʀO'Bʀɪᴇɴ yes exactly

CSᵠ

@CᴏɴᴏʀO'Bʀɪᴇɴ ith

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:27 PM

@CSᵠ kth

CSᵠ

zth

anOKsquirrel

jth

Martin Büttner

@Zgarb open problem in the sense that there is no general known condition. or open in the sense that there are certain clusters for which we don't even know how to figure it out algorithmically by brute force?

@NathanMerrill ^ the latter would make your challenge slightly impossible

Nathan Merrill

you mean my last tiling?

TimmyD

array / (something) should return an array of arrays, sliced by thesomething (either literal if it's numeric, or length-of-string, etc.)

if it doesn't divide evenly, the last array is truncated

Martin Büttner

5:28 PM

@NathanMerrill oh you're not even asking for gap-free tilings

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@TimmyD Show me an example?

My mind isn't working right now :P

Nathan Merrill

no, minimizing the gaps

TimmyD

[1,2,3,4,5] / 2 ==> [[1,2],[3,4],[5]]

anOKsquirrel

how minimized?

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@TimmyD ohhhhhh

Nathan Merrill

5:29 PM

as possible?

TimmyD

you could do floats, too

CSᵠ

@TimmyD nice

Martin Büttner

@NathanMerrill in the 30x30 block, or in terms of density?

anOKsquirrel

@NathanMerrill how can you calculate the most optimal?

TimmyD

[1,2,3,4,5] / 2.5 ==> [[1,2,3],[4,5]]

CSᵠ

5:30 PM

[1,2,3,4,5,6]:2=[2,4,6]

Nathan Merrill

@MartinBüttner either sounds fine. If density is near impossible, then 30x30 block

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@TimmyD Rounded up?

VoteToClose

@CSᵠ Yeah - Raspbian distros come with Mathematica installed now.

Martin Büttner

@NathanMerrill there's another thing: do the tilings have to be regular?

TimmyD

[1,2,3,4,5,6,7,8,9,10] / 2.5 ==> [[1,2,3],[4,5],[6,7,8],[9,10]]

Sherlock9

5:30 PM

Welp, having looked at sums of p-th powers == n, I'm going truncate the possible p to 2<=p<=4

Even fifth powers are too much @_@

Nathan Merrill

@MartinBüttner I'm pretty positive that an optimal tiling is going to be regular

Martin Büttner

^ I was wondering about that, but I don't actually know

well I mean, I can think of optimal irregular tilings, but then a regular one exists as well

Nathan Merrill

especially because we aren't allowing rotation or reflection

CSᵠ

@VoteToClose $2,745 or 300/yr ?!?!??! for free in a distro?

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@TimmyD So... alternating round up/down?

Nathan Merrill

5:32 PM

well, we've never come up with an irregular tiling that couldn't be converted into a regular one

Martin Büttner

@CSᵠ yes, Mathematica's been on the pi for a couple of years now

VoteToClose

@CSᵠ raspberrypi.org/blog/mathematica-10

TimmyD

@CᴏɴᴏʀO'Bʀɪᴇɴ Well, in that instance, because 2.5*2=5 so you get a cycle

CSᵠ

@CᴏɴᴏʀO'Bʀɪᴇɴ discard float, treat as int (floor)

Martin Büttner

@NathanMerrill there's no conversion here, because you're prescribing the prototile

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:33 PM

@TimmyD Huh. Is there an existing implementation?

Stefnotch

*reads the chat*
*gives up, 2 (or more?) conversations at the same time*

VoteToClose

It was the main reason for me attempting to emulate a raspberry pi. xD

Martin Büttner

prototile XO, optimal irregular tiling:

VoteToClose

Which failed miserably, of course.

Martin Büttner

XOXOXO
XOXOXO
OXOXOX
XOXOXO
OXOXOX
OXOXOX

VoteToClose

5:33 PM

But still.

Martin Büttner

I can even tile that aperiodically by using a Fibonacci tiling to alternate between offsets

Sherlock9

@MartinBüttner Having read that message without context, I thought "on the pi" meant "gone loopy"

Nathan Merrill

oooh, I understand

VoteToClose

@CSᵠ I see that CG has taken your interest, since you haven't left yet.

Martin Büttner

@Sherlock9 this is also true.

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:34 PM

@Stefnotch I'm talking with @TimmyD and @CSᵠ; @MartinBüttner is talking to @Sherlock9 and @NathanMerrill; @VoteToClose is talking to himself ;)

anOKsquirrel

do raspberry pi zeroes also have mathematica?

CSᵠ

@VoteToClose it sparked a something, had it in me for ages

Nathan Merrill

however, because every prototile can converted into a square tile (without changing the tiling), I think it is safe to say that the optimal tiling is going to be regular

CSᵠ

had to get rid of the "skills" for business, readability seems important for office folk, sigh :PP

TimmyD

@CᴏɴᴏʀO'Bʀɪᴇɴ You'd get a different cycle if you ` / 2.75` ... maybe something like [[1,2,3],[4,5,6],[7,8],[9,10]]

Martin Büttner

5:36 PM

@NathanMerrill re your edit, I think you should still explicitly mention whether your counting that ratio inside the 30x30 block or in the infinite plane

Sherlock9

@VoteToClose @CSᵠ I used to do those projects where you factor really large numbers, because messing around with code for factoring was really fun. Now CG fills that coding-shaped hole in my life

Nathan Merrill

@MartinBüttner is it going to be near impossible to do it in the infinite plane?/

Martin Büttner

also, yes it may be true that regular tilings are always optimal, but that doesn't answer whether submissions may produce irregular ones if they give the same ratio ;)

TimmyD

Or, like @CSᵠ said, just drop the decimal positions and floor the divisor

VoteToClose

@CᴏɴᴏʀO'Bʀɪᴇɴ Yeah, of course I'm talking to myself. Why wouldn't I?

Nathan Merrill

5:36 PM

@MartinBüttner yes irregular ones are acceptable

Martin Büttner

@NathanMerrill I think you'll have to ask someone like Zgarb or Peter to tell you that.

VoteToClose

@VoteToClose Stop talking to him - you're making me jealous.

@VoteToClose Oh, hush, you.

Cᴏɴᴏʀ O'Bʀɪᴇɴ

xD

Nathan Merrill

well, if it is going to require their input, then 30x30 it is

VoteToClose

@VoteToClose I think we should stop speaking now.

Nathan Merrill

5:37 PM

I don't want this to be a "genius-only" challenge

CSᵠ

@Sherlock9 i verbosely hardcoded the output of everything constant

VoteToClose

@VoteToClose Ugh, fine.

TimmyD

@CᴏɴᴏʀO'Bʀɪᴇɴ I can't think of a directly-the-same existing implementation, but slicing an array is decently standard in many language

Martin Büttner

@NathanMerrill I don't know how difficult it would actually be, but I can't spend much time thinking about it right now

Sherlock9

@CSᵠ Sorry?

Nathan Merrill

5:38 PM

@MartinBüttner that's fine

Zgarb

@MartinBüttner In the former sense, I believe. If there is a smallest known possible counterexample, it's got to be huge.

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@TimmyD I can do it by flooring, but the decimal bit stumps me.

CSᵠ

@Sherlock9 apology accepted.

VoteToClose

Truncating to int in Vitsy suuucks.

D1M-

Sherlock9

@CSᵠ No, wait. Hardcoded the output of what?

anOKsquirrel

5:39 PM

sorry, whenever I see someone say x in y sucks I just see y sucks

VoteToClose

ಠ_ಠ

Sherlock9

@VoteToClose You're writing the bloody language. Fix it

VoteToClose

I am righting it, but that's how I wrote it.

anOKsquirrel

righting haha

CSᵠ

@Sherlock9 say hour in seconds would always be 3600, and not a 60*60 expr

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:40 PM

@VoteToClose pnt is truncate in Jolf

VoteToClose

@Sherlock9 Righting was actually contextually correct in this case: to right something in England means to fix, to set to a position in which it is not "wonky".

CSᵠ

@anOKsquirrel regex in javascript sux!

anOKsquirrel

> javascript sux

VoteToClose

> wonky

Nathan Merrill

@MartinBüttner actually, tiling does need to be regular, because if I'm measuring minimum number of spaces in a fixed area, I may be able to remove a space or two by making the edges irregular

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:41 PM

@CSᵠ ಠ_ಠ cc @anOKsquirrel

VoteToClose

Alrighty. I must leave.

I hunger.

TimmyD

@CᴏɴᴏʀO'Bʀɪᴇɴ Like, you need to "accumulate" the decimal part until you have enough to include an additional element in the sliced array.

VoteToClose

And need to go home.

Sherlock9

@VoteToClose Fair enough. I still edited my message to what I meant first

Cᴏɴᴏʀ O'Bʀɪᴇɴ

Goodbye.

Sherlock9

5:41 PM

@VoteToClose Bye

anOKsquirrel

@CSᵠ better than python

quintopia

bentomonsters.com/2015/10/panda-penguin-sushi.html

TimmyD

Whether you do that by rounding or by literally accumulating is up to the implementation.

quintopia

IT is important that you have this sushi in your life

Sherlock9

@anOKsquirrel Didn't the regex module do better?

quintopia

5:42 PM

anOKsquirrel

@Sherlock9 who wants imports to do regexes?

Sherlock9

@anOKsquirrel What's your opinion of Ruby regexes?

CSᵠ

@anOKsquirrel nope, py has backref, js knows not what those are

Martin Büttner

@NathanMerrill you are aware though that you can also change the number of spaces by a simple translation if the period of the tiling doesn't divide 30?

anOKsquirrel

@Sherlock9 ruby sux

Nathan Merrill

5:42 PM

@MartinBüttner correct

Martin Büttner

@anOKsquirrel wat

TimmyD

[1,2,3,4,5,6,7,8,9] / (4/3) ==> [[1],[2,3],[4,5],[6],[7,8],[9,10]] could be an example

CSᵠ

@anOKsquirrel got a point there, even more in cg

anOKsquirrel

@MartinBüttner for code golfing that is

Martin Büttner

@CSᵠ it does

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:43 PM

@TimmyD Oh!

Martin Büttner

but it doesn't have lookbehinds

CSᵠ

@TimmyD why would you want that?

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@MartinBüttner That be true

TimmyD

@CSᵠ Why? I dunno. Why are you dividing an array by a float in the first place? ;-)

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@TimmyD except there is no 10

Martin Büttner

5:44 PM

@TimmyD because [1,2,3,4,5,6] / 0.5 == [[1,2,3],[4,5,6]]

TimmyD

@CᴏɴᴏʀO'Bʀɪᴇɴ handwave

CSᵠ

@TimmyD @CᴏɴᴏʀO'Bʀɪᴇɴ [1,2,3,4,5,6,7,8,9] / (4,3,1) = [[1,2,3,4],[5,6,7],[8],[9]]

Sherlock9

@MartinBüttner Dividing by half is multiplying by 2, for gosh sake

Cᴏɴᴏʀ O'Bʀɪᴇɴ

@CSᵠ Nice idea thanks

Martin Büttner

@Sherlock9 in your maths maybe

anOKsquirrel

5:45 PM

@Sherlock9 math != programming

codegolf*

quintopia

@TimmyD I have no idea what is happening here

CSᵠ

@MartinBüttner sorry, that's what i meant

TimmyD

@MartinBüttner [1,2,3,4,5,6] / 0.5 == [1,2,3,4,5,6] / 2 ??

Cᴏɴᴏʀ O'Bʀɪᴇɴ

math INTERSECT programming != {}

Sherlock9

No because programming doesn't have half the consistency of math

Martin Büttner

5:46 PM

@Sherlock9 they aren't too bad. I think they've got recursion.

Sherlock9

@MartinBüttner Really? How does that work?

CSᵠ

@CᴏɴᴏʀO'Bʀɪᴇɴ ymw

Martin Büttner

@TimmyD [1,2,3,4,5,6] / 2 == [[1,2],[3,4],[5,6]]

@Sherlock9 just like in Perl/PCRE

you reference some group in your pattern, and that pattern is matched again

Sherlock9

Ah

Martin Büttner

as opposed to backreference which match the exact same string again, recursion actually processes the pattern again

Sherlock9

5:47 PM

@MartinBüttner I don't know Perl so thanks for the explanation

TimmyD

@quintopia The first sliced array has length (1.33333....), which isn't enough for two elements, so we take only one, leaving (0.3333...) remaining. The second sliced array has length (1.3333... + 0.3333 = 1.6666...), which is enough for two elements.

Martin Büttner

it's actually more useful for pattern reuse than recursion, because if you're doing recursion in your regex (in production code), there's a good chance you should be doing something else

CSᵠ

it's not pearl

TimmyD

@MartinBüttner Oh, right. Getting myself confused

CSᵠ

@TimmyD that's gonna give you headaches and garbage

Cᴏɴᴏʀ O'Bʀɪᴇɴ

5:48 PM

@TimmyD It's enough for 2 elements because why?

TimmyD

@CSᵠ Yes. Which is why I recommended flooring the divisor

Sherlock9